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Question

Allan, Bernice, Candice and Derrick shared the cost of a present. The amount Allan paid is 1/14 of the total amount Bernice and Candice paid. The amount Bernice paid is 1/4 of the total amount Candice and Derrick paid. The amount Derrick paid is twice the amount Candice paid. Given that Candice paid $63 more than Allan, how much was the cost of the present?

Answer 1

A=(B+C)/14

B= (C+D)/4

D=2C

C=63+A

A=((C+D)/4 + C)/14 = C/56 + D/56 + C/14

A = 5C/56 + D/56 = 5C/56 + 2C/56 = 7C/56

C-63 = 7C/56

56C/56 -7C/56 = 63

49C/56 = 7C/8 = 63

C/8 = 9

C =72

D= 2C = 144

B = (C+D)/4 = (72 +144)/4 = 18+36 = 54

B= 54

A = (B+C)/14 = (54+72)/14 = 126/14 = 63/7 = 9

A=9

A=9

B=54

C = 72

D = 144

Cost of the present = A+B+C+D = 9+54+72+144= 279

= $279